Does Some Deeper Level of Physics Underlie Quantum Mechanics?
An Interview with Nobelist Gerard 't Hooft
By George Musser, October 7, 2013

(Look for a summary of his theory at: Gerard 't Hooft, The cellular automation interpretation of quantum mechanics; https://arxiv.org/abs/1405.1548v2 (Submitted on 7 May 2014 (v1), last revised 10 Jun 2014 (this version, v2))
When investigating theories at the tiniest conceivable scales in nature, 'quantum logic' is taking over from 'classical logic' in the minds of almost all researchers today. Dissatisfied, the author investigated how one can look at things differently. This report is an overview of older material, but also contains many new observations and calculations.
Quantum mechanics is looked upon as a tool, not as a theory. Examples are displayed of models that are classical in essence, but can be analysed by the use of quantum techniques, and we argue that even the Standard Model, together with gravitational interactions, may be viewed as a quantum mechanical approach to analyse a system that could be classical at its core. We then explain how these apparently heretic thoughts can be reconciled with Bell's theorem and the usual objections voiced against the notion of 'super determinism'. Our proposal would eradicate the collapse problem and the measurement problem.)

The interview:
Vienna - Over the past several days, I attended a fascinating conference that explored an old idea of Einstein's, one that was largely dismissed for decades: that quantum mechanics is not the root level of reality, but merely a hazy glimpse of something even deeper.
A leading advocate is Gerard 't Hooft of Utrecht University, who shared the 1999 Physics Nobel for helping to assemble the Standard Model of particle physics (for which, rumor has it, another Nobel will be awarded tomorrow). He and I chatted over a lunch of beef goulash and maize stew, and I thought you'd be intrigued by what he had to say.
't Hooft thinks the notorious randomness of quantum mechanics is just a front. Underneath, the world obeys perfectly sensible rules. In the models he has toyed with, those rules govern building blocks even more fundamental than particles. You'd see them only if you could zoom into the so-called Planck scale, which, according to many modern theories, is the smallest meaningful distance in nature.
One point in favor of such an approach is that far-flung particles can act in a coordinated way (kwantumverstrengeling), which you wouldn't expect if they were purely random.
Yet the idea of a deeper level is deeply troubled. In the 1960s, Irish physicist John Bell showed that the degree of coordination among particles is too exacting for any deeper level of physics to explain. Bell argued that particles actively need to communicate with one another, which 't Hooft's models don't allow for.

Superdeterminism
When I first chatted with 't Hooft for an article eight years ago, he told me he wasn't sure how to evade Bell's reasoning. Since then, he has sought to jump through a loophole known as superdeterminism. It's a weird and downright disturbing idea. Only three other people I know support it, notably Sabine Hossenfelder of the Nordic Institute of Theoretical Physics, who blogged her views last week.
The sober way to put it is that physicists are never able to conduct a fully controlled experiment, since the experimental setup they choose is not strictly independent of the processes that created the particles. Even if the experimentalists (conventionally named Alice and Bob) live on Earth and the particles come from quasars billions of light-years away, they share a common past in the very early universe. Their subtle interdependence creates a selection bias, misleading physicists into thinking that no deeper level of physics could explain the particle coordination, when in fact it could.

The dramatic version is that free will is an illusion. Worse, actually. Even regular determinism - without the "super" - subverts our sense of free will. Through the laws of physics, you can trace every choice you make to the arrangement of matter at the dawn of time. Superdeterminism adds a twist of the knife. Not only is everything you do preordained, the universe reaches into your brain and stops you from doing an experiment that would reveal its true nature. The universe is not just set up in advance. It is set up in advance to fool you. As a conspiracy theory, this leaves Roswell and the Priory of Sion in the dust.
That said, one person's conspiracy is another's law of physics. Lots of things in the world seem conspiratorial at first glance, but are the result of well-established principles. The fact the moon spins on its axis at exactly the same rate it orbits Earth (thereby keeping the same face to us, or nearly so) is not the work of a cabal, but of laws such as the conservation of angular momentum. In the opening panel discussion of the conference, 't Hooft speculated that some new law of physics might harmonize particles' properties with humans' measurement choices: "What looks like a conspiracy today may be due to a conservation law we don't know about today... It's incredible until you find it's mathematical necessity."
What follows is an abridged transcript of our lunchtime chat.

GM: What's the problem with quantum mechanics?
GtH: Quantum mechanics as it stands would be perfect if we didn't have the quantum-gravity issue and a few other very deep fundamental problems. I want to understand what will happen to the Standard Model as we pursue higher energies, I want to understand what quantum mechanics is about, and I want to understand how gravity works. The suspicion is, probably, answers will come as a package. You can't just solve one problem without touching the others; they're probably related. Maybe you have to solve all problems in one giant stroke. If that's the case, then you have a long fight ahead of us, because it's going to be very difficult.

GM: Can you describe your theory?
GtH: The theory is that you have something classical underlying quantum mechanics, obeying totally classical laws of nature - classical, meaning it looks like solving the classical planetary system or billiard balls or anything large-scale - except that ordinary classical theories are based on the real numbers. I'm not excluding real numbers as a good basis for a classical theory, but I'm also considering other options, such as the integers or, even better, numbers that form a finite set. I think I need finiteness at all levels of an ultimate theory.

GM: That's motivated by Planckian discreteness?
GtH: Yes. At the Planck scale, it's likely that you only deal with Boolean variables and integers, because that's what the holographic principle of black holes seems to be telling us - that the amount of information on the black hole horizon is actually finite.

GM: Last night, you gave an example of your underlying classical model as almost like a chessboard.
GtH: That's just an example of a problem where the question is a perfectly classical question, the answer is a perfectly classical answer, but the way to get the answer is by using quantum mechanics. Quantum mechanics is just a tool - and an extremely useful tool. That's the way I think quantum mechanics has to be looked at.
When I consider a classical theory, and I give it a quantum wavefunction just because I use quantum mechanics as a tool, that wavefunction automatically collapses when I do a measurement. When you do a Schrödinger cat experiment, the outcome of the cat will be either alive or dead, but never in between.

GM: So, in this sense, superposition is a mental construct, whereas the real world doesn't really have that. We created a problem by our choice of this convenient tool of quantum mechanics to do our statistics for us.
GtH: Yes, there's no superposition. The only superpositions are in our way of describing what's going on. For very good reason: we can make transformations such that we can describe the vacuum as a single state. In reality, the vacuum is probably a very complex, fluctuating mode. If you make superpositions, you can make a single state look like the vacuum.

GM: I was quite taken by the examples you gave of how you can get apparently quantum behavior from a classical system. Do you think that our universe is governed by extremely simple laws that then become complicated because there's so many degrees of freedom?
GtH: Well, that's the hope. There's no guarantee that it's true. Nature's laws seem to be so universal, with such a sense of internal logic in them, that maybe the ultimate law is very simple and straightforward.

GM: Do you think the very simple law should be a local law?
GtH: Basically yes. I think locality will be an essential ingredient. You have to understand why things happening here are independent of things happen there. If you don't assume such a thing, then it gets a lot harder to understand how laws of nature are working. Then nature's bookkeeping system seems to be complex again. I want a bookkeeping system that tells you what happens here just depends on a few bits of information right here.

GM: Apart from locality, what other basic principles are really vital?
GtH: Well, causality - the fact there's a strict separation between cause and effect. I want a theory in which everything that happens has a cause. The decay of an atom is caused by deterministic laws. Today, we only know its statistical laws, but ultimately you should be able to point at a definite cause: this is why the atom decayed today. Something in its environment happened.

GM: Ordinarily, we think that Bell's theorem would rule out a classical model. So, how do we overcome that issue?
GtH: Yes, that's not easy. I do not have the complete answer, because whatever answer I think of, I am always the first to criticize. The only answer I can come up with today is that there are correlations all over, presumably because the entire universe started with a single big bang. Everybody in our universe has a common past, and so they are correlated. The photons emitted by a quasar are correlated with the photons emitted by another quasar. It's not true those quasars are independent.
That could be the answer to Bell. You can do the exercise. You can ask about a source emitting photons and the ancestors of Alice and Bob. While the source emits photons, Alice and Bob have not yet been born. They are many, many light-years away from each other. Those ancestors - the atoms in them - eventually cause Alice and Bob to make their decisions. Those atoms are correlated with the atoms of the source. Everything is correlated with everything else - not a little bit, but very, very strongly.

GM: Did you ever meet John Bell?
GtH: I think it was in the early '80s. I raised the question: Suppose that also Alice's and Bob's decisions have to be seen as not coming out of free will, but being determined by everything in the theory. John said, well, you know, that I have to exclude. If it's possible, then what I said doesn't apply. I said, Alice and Bob are making a decision out of a cause. A cause lies in their past and has to be included in the picture.
But most physicists refuse to consider that as an essential element, and I very well understand why. Once you have a physical theory, that tells you the outcome of a physical measurement based on what Alice and Bob decide to measure. If they measure this or they measure that, our theory should tell us what they will see. Our theory should not bother about why Alice and Bob make this or that measurement. That is perfectly natural for today's physics. But then you will not be able to answer the question of what quantum mechanics is. You must realize that Alice and Bob are not making that decision out of free will. That free will is actually embedded in the complexity of the atoms in their brains. The world is so complex that nobody can predict what their decision will be, but nevertheless, whatever their decisions will be, they will be a consequence of the laws of nature.

GM: Most people can accept that our experimental decisions are determined, but the degree of freedom that determine them are usually taken as independent from the degrees of freedom of the system we're studying.
GtH: Then you're stuck not only with Bell's inequalities, but more generally with the whole quantum picture of reality. So, I think you have to assume that Bob has made a decision not out of free will, but by some predetermined correlation.
In quantum physics, there's a notion of counterfactual measurement. You measure what happens if I put the polarizer this way, and then you ask, what if I had it that way? In my opinion, that is basically illegal. There's only one thing you can measure.

GM: What's the current direction you're taking in your research?
GtH: First of all, I'm writing things down. What I discover is, when I write things down, it forces me to think about things much deeper than I did in the past, and I get new ideas. Things I have in my mind sound very simple, but when you attempt to write them down, they become more complicated and force me to think about them.
Right now, I work on two projects. One is quantum mechanics; the other is quantum gravity. Conformal symmetry [insensitivity to absolute scale] is a much more important symmetry with quantum gravity than people usually think. So, I'm trying to build conformal symmetry into a theory of quantum gravity, and while doing so, for a moment I'll forget the quantum mechanics problem. The reason we have scales today is because conformal symmetry is spontaneously broken. That's why atoms have sizes and clocks have rates at which they tick.
For instance, the universe must have had a period of inflation - that was a period when conformal symmetry was working very, very well. The universe looks like it was in a mode when it was conformally symmetric for a while. How do we embed that in a proper way in the rest of our understanding of nature?

GM: As a student, you learn the full mathematical machinery of quantum mechanics and the usual interpretation that goes along with it. What caused you personally to begin to question that? So many students don't question that.
GtH: I'm asking questions all the time. One of the questions I'm asking all the time is: Are we doing things right? Am I doing things right? The books that I read, are they correct? Maybe I'm wrong in some basic way. I know that I'm not entirely correct because I haven't got the correct theory. But I continue asking questions.